A constant speed motion is one in which equal distances are covered in equal times
The bird travels a cumulative distance of 7.[tex]\overline 3[/tex] km
The reason the above value is correct is as follows:
The known parameters are;
Speed of the runner, [tex]v_r[/tex] = 2.1 km/hr
The location where the bird begins to fly to the finish line = When the runner is 4.4 km from the finish line
The speed of the bird, [tex]v_b[/tex] = 10.5 km/hr = 5 times the runners speed
The bird reaches the finish line, turns, and returns back to the runner
Required:
The find cumulative distance traveled by the bird
Solution:
The distance the bird travels is five times the distance the runner travels, therefore,
Let x represent the distance the runner ravels before the bird returns, we have;
The distance the bird travels = 4.4 + 4.4 - x = 8.8 - x
The distance the runner travels = x
The time the runner runs x km = The time the bird flies (8.8 - 4) km
[tex]From \ velocity = \dfrac{Distance }{Time}[/tex], we have;
[tex]Time= \dfrac{Distance }{Velocity}[/tex]
Given the time taken by the runner is equal to the time taken by bird, while running, we have;
[tex]Time= \dfrac{x}{2.1} = \dfrac{8.8 - x}{10.5}[/tex]
Therefore;
10.5·x = 2.1·(8.8 - x) = 2.1×8.8 - 2.1·x
10.5·x + 2.1·x = 2.1×8.8 = 18.84
12.6·x = 18.84
[tex]x = \dfrac{18.84}{12.6} =\dfrac{22}{15} = 1.4 \overline 6[/tex]
[tex]The \ distance \ the \ bird \ travels = 8.8 - \dfrac{22}{15} \approx \dfrac{22}{3} = 7. \overline 3[/tex]
The cumulative distance the bird travels is 7.[tex]\overline 3[/tex] km
Learn more about constant speed motion here:
https://brainly.com/question/12684433
